A divide and conquer method for unitary and orthogonal eigenproblems

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dc.contributor.authorGragg, William B.
dc.contributor.authorReichel, Lother
dc.contributor.corporateOperations Research (OR)
dc.contributor.corporateGraduate School of Operational and Information Sciences (GSOIS)
dc.contributor.departmentMathematicsen_US
dc.date1989-02
dc.date.accessioned2013-03-07T21:52:34Z
dc.date.available2013-03-07T21:52:34Z
dc.date.issued1989-02
dc.description.abstractLet H epsilon C be a unitary upper Hessenberg matrix whose eigenvalues, and possibly also eigenvectors, are to be determined. We describe how this eigenproblem can be solved by a divide and conquer method, in which the matrix H is split into two smaller unitary right Hessenberg matrices H1 and H2 by a rank-one modification of H. The eigenproblems for H1 and H2 can be solved independently, and the solutions of these smaller eigenproblems define a rational function, whose zeros on the unit circle are the eigenvalues of H. The eigenvectors of H can be determined from the eigenvalues of H and the eigenvectors of H1 and H2. The outlined splitting of unitary upper Hessenberg matrices into smaller such matrices is carried out recursively. This gives rise to a divide and conquer method that is suitable for implementation on a parallel computer. When H epsilon R sub nxn is orthogonal, the divide and conquer scheme simplifies and is described separately. Our interest in the orthogonal eigenproblem stems from applications in signal processing. Numerical examples for the orthogonal eigenproblem conclude the paperen_US
dc.description.distributionstatementApproved for public release; distribution is unlimited.
dc.description.funderO&MN, Direct Fundingen_US
dc.description.sponsorshipThis report was prepared in conjunction with research conducted for the National Science Foundation and for the Naval Postgraduate School Research Council and funded by the Naval Postgraduate School Research Council.en_US
dc.description.urihttp://archive.org/details/divideconquermet00grag
dc.identifier.npsreportNPS-53-89-007
dc.identifier.urihttps://hdl.handle.net/10945/29823
dc.language.isoen_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.authorunitary eigenproblem, orthogonal eigenproblem, divide and conquer, parallel algorithm, Pisarenko frequencies, Gauss-Szego quadrature.en_US
dc.subject.authorUnitary eigenproblemen_US
dc.subject.authorOrthogonal eigenproblemen_US
dc.subject.authorDivide and conqueren_US
dc.subject.authorParallel algorithmen_US
dc.subject.authorPisarenko frequenciesen_US
dc.subject.authorGauss-szego quadratureen_US
dc.subject.lcshEIGENVALUESen_US
dc.titleA divide and conquer method for unitary and orthogonal eigenproblemsen_US
dc.typeTechnical Reporten_US
dspace.entity.typePublication
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relation.isOrgUnitOfPublication.latestForDiscoverydd7f1b97-9c92-402d-b910-27f080946cde
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